1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 145,953 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  2 111       2020-03-18 fema… 0-18  e380000… nhs_bed…    27 mk454hr  East of E…
##  3 111       2020-03-18 fema… 0-18  e380000… nhs_bla…     9 bb12fd   North West
##  4 111       2020-03-18 fema… 0-18  e380000… nhs_bro…    11 br33ql   London    
##  5 111       2020-03-18 fema… 0-18  e380000… nhs_can…     9 ws111jp  Midlands  
##  6 111       2020-03-18 fema… 0-18  e380000… nhs_cit…    12 n15lz    London    
##  7 111       2020-03-18 fema… 0-18  e380000… nhs_enf…     7 en40dy   London    
##  8 111       2020-03-18 fema… 0-18  e380000… nhs_ham…     6 dl62uu   North Eas…
##  9 111       2020-03-18 fema… 0-18  e380000… nhs_har…    24 ts232la  North Eas…
## 10 111       2020-03-18 fema… 0-18  e380000… nhs_kin…     6 kt11eu   London    
## # … with 145,943 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##     date_report               nhs_region deaths
## 1    2020-03-01          East of England      0
## 2    2020-03-02          East of England      1
## 3    2020-03-03          East of England      0
## 4    2020-03-04          East of England      0
## 5    2020-03-05          East of England      0
## 6    2020-03-06          East of England      1
## 7    2020-03-07          East of England      0
## 8    2020-03-08          East of England      0
## 9    2020-03-09          East of England      1
## 10   2020-03-10          East of England      0
## 11   2020-03-11          East of England      0
## 12   2020-03-12          East of England      0
## 13   2020-03-13          East of England      1
## 14   2020-03-14          East of England      2
## 15   2020-03-15          East of England      2
## 16   2020-03-16          East of England      1
## 17   2020-03-17          East of England      1
## 18   2020-03-18          East of England      5
## 19   2020-03-19          East of England      4
## 20   2020-03-20          East of England      2
## 21   2020-03-21          East of England     11
## 22   2020-03-22          East of England     12
## 23   2020-03-23          East of England     11
## 24   2020-03-24          East of England     19
## 25   2020-03-25          East of England     26
## 26   2020-03-26          East of England     36
## 27   2020-03-27          East of England     38
## 28   2020-03-28          East of England     28
## 29   2020-03-29          East of England     43
## 30   2020-03-30          East of England     45
## 31   2020-03-31          East of England     70
## 32   2020-04-01          East of England     62
## 33   2020-04-02          East of England     64
## 34   2020-04-03          East of England     80
## 35   2020-04-04          East of England     71
## 36   2020-04-05          East of England     76
## 37   2020-04-06          East of England     71
## 38   2020-04-07          East of England     93
## 39   2020-04-08          East of England    111
## 40   2020-04-09          East of England     87
## 41   2020-04-10          East of England     74
## 42   2020-04-11          East of England     91
## 43   2020-04-12          East of England    101
## 44   2020-04-13          East of England     78
## 45   2020-04-14          East of England     61
## 46   2020-04-15          East of England     82
## 47   2020-04-16          East of England     74
## 48   2020-04-17          East of England     86
## 49   2020-04-18          East of England     64
## 50   2020-04-19          East of England     67
## 51   2020-04-20          East of England     67
## 52   2020-04-21          East of England     75
## 53   2020-04-22          East of England     67
## 54   2020-04-23          East of England     49
## 55   2020-04-24          East of England     66
## 56   2020-04-25          East of England     54
## 57   2020-04-26          East of England     48
## 58   2020-04-27          East of England     46
## 59   2020-04-28          East of England     58
## 60   2020-04-29          East of England     32
## 61   2020-04-30          East of England     45
## 62   2020-05-01          East of England     49
## 63   2020-05-02          East of England     29
## 64   2020-05-03          East of England     41
## 65   2020-05-04          East of England     19
## 66   2020-05-05          East of England     36
## 67   2020-05-06          East of England     30
## 68   2020-05-07          East of England     33
## 69   2020-05-08          East of England     33
## 70   2020-05-09          East of England     29
## 71   2020-05-10          East of England     22
## 72   2020-05-11          East of England     18
## 73   2020-05-12          East of England     21
## 74   2020-05-13          East of England     27
## 75   2020-05-14          East of England     26
## 76   2020-05-15          East of England     19
## 77   2020-05-16          East of England     26
## 78   2020-05-17          East of England     17
## 79   2020-05-18          East of England     25
## 80   2020-05-19          East of England     15
## 81   2020-05-20          East of England     26
## 82   2020-05-21          East of England     21
## 83   2020-05-22          East of England     13
## 84   2020-05-23          East of England     12
## 85   2020-05-24          East of England     16
## 86   2020-05-25          East of England     25
## 87   2020-05-26          East of England     14
## 88   2020-05-27          East of England     12
## 89   2020-05-28          East of England     17
## 90   2020-05-29          East of England     15
## 91   2020-05-30          East of England      9
## 92   2020-05-31          East of England      8
## 93   2020-06-01          East of England     17
## 94   2020-06-02          East of England     14
## 95   2020-06-03          East of England     10
## 96   2020-06-04          East of England      7
## 97   2020-06-05          East of England     12
## 98   2020-06-06          East of England      4
## 99   2020-06-07          East of England      9
## 100  2020-06-08          East of England      5
## 101  2020-06-09          East of England      4
## 102  2020-06-10          East of England      7
## 103  2020-06-11          East of England      0
## 104  2020-06-12          East of England      5
## 105  2020-06-13          East of England      2
## 106  2020-03-01                   London      0
## 107  2020-03-02                   London      0
## 108  2020-03-03                   London      0
## 109  2020-03-04                   London      0
## 110  2020-03-05                   London      0
## 111  2020-03-06                   London      1
## 112  2020-03-07                   London      1
## 113  2020-03-08                   London      0
## 114  2020-03-09                   London      1
## 115  2020-03-10                   London      0
## 116  2020-03-11                   London      7
## 117  2020-03-12                   London      6
## 118  2020-03-13                   London     10
## 119  2020-03-14                   London     14
## 120  2020-03-15                   London     10
## 121  2020-03-16                   London     18
## 122  2020-03-17                   London     25
## 123  2020-03-18                   London     31
## 124  2020-03-19                   London     25
## 125  2020-03-20                   London     44
## 126  2020-03-21                   London     50
## 127  2020-03-22                   London     54
## 128  2020-03-23                   London     64
## 129  2020-03-24                   London     87
## 130  2020-03-25                   London    113
## 131  2020-03-26                   London    130
## 132  2020-03-27                   London    130
## 133  2020-03-28                   London    122
## 134  2020-03-29                   London    147
## 135  2020-03-30                   London    150
## 136  2020-03-31                   London    181
## 137  2020-04-01                   London    202
## 138  2020-04-02                   London    190
## 139  2020-04-03                   London    196
## 140  2020-04-04                   London    230
## 141  2020-04-05                   London    195
## 142  2020-04-06                   London    198
## 143  2020-04-07                   London    219
## 144  2020-04-08                   London    238
## 145  2020-04-09                   London    206
## 146  2020-04-10                   London    170
## 147  2020-04-11                   London    177
## 148  2020-04-12                   London    158
## 149  2020-04-13                   London    166
## 150  2020-04-14                   London    144
## 151  2020-04-15                   London    142
## 152  2020-04-16                   London    139
## 153  2020-04-17                   London    100
## 154  2020-04-18                   London    101
## 155  2020-04-19                   London    103
## 156  2020-04-20                   London     95
## 157  2020-04-21                   London     95
## 158  2020-04-22                   London    108
## 159  2020-04-23                   London     77
## 160  2020-04-24                   London     71
## 161  2020-04-25                   London     58
## 162  2020-04-26                   London     53
## 163  2020-04-27                   London     51
## 164  2020-04-28                   London     43
## 165  2020-04-29                   London     44
## 166  2020-04-30                   London     40
## 167  2020-05-01                   London     41
## 168  2020-05-02                   London     40
## 169  2020-05-03                   London     36
## 170  2020-05-04                   London     30
## 171  2020-05-05                   London     25
## 172  2020-05-06                   London     37
## 173  2020-05-07                   London     37
## 174  2020-05-08                   London     29
## 175  2020-05-09                   London     23
## 176  2020-05-10                   London     26
## 177  2020-05-11                   London     18
## 178  2020-05-12                   London     18
## 179  2020-05-13                   London     16
## 180  2020-05-14                   London     20
## 181  2020-05-15                   London     18
## 182  2020-05-16                   London     14
## 183  2020-05-17                   London     15
## 184  2020-05-18                   London      9
## 185  2020-05-19                   London     13
## 186  2020-05-20                   London     19
## 187  2020-05-21                   London     12
## 188  2020-05-22                   London     10
## 189  2020-05-23                   London      6
## 190  2020-05-24                   London      7
## 191  2020-05-25                   London      9
## 192  2020-05-26                   London     12
## 193  2020-05-27                   London      7
## 194  2020-05-28                   London      8
## 195  2020-05-29                   London      7
## 196  2020-05-30                   London     12
## 197  2020-05-31                   London      6
## 198  2020-06-01                   London     10
## 199  2020-06-02                   London      7
## 200  2020-06-03                   London      6
## 201  2020-06-04                   London      8
## 202  2020-06-05                   London      3
## 203  2020-06-06                   London      0
## 204  2020-06-07                   London      4
## 205  2020-06-08                   London      5
## 206  2020-06-09                   London      2
## 207  2020-06-10                   London      7
## 208  2020-06-11                   London      5
## 209  2020-06-12                   London      0
## 210  2020-06-13                   London      0
## 211  2020-03-01                 Midlands      0
## 212  2020-03-02                 Midlands      0
## 213  2020-03-03                 Midlands      1
## 214  2020-03-04                 Midlands      0
## 215  2020-03-05                 Midlands      0
## 216  2020-03-06                 Midlands      0
## 217  2020-03-07                 Midlands      0
## 218  2020-03-08                 Midlands      3
## 219  2020-03-09                 Midlands      1
## 220  2020-03-10                 Midlands      0
## 221  2020-03-11                 Midlands      2
## 222  2020-03-12                 Midlands      6
## 223  2020-03-13                 Midlands      5
## 224  2020-03-14                 Midlands      4
## 225  2020-03-15                 Midlands      5
## 226  2020-03-16                 Midlands     11
## 227  2020-03-17                 Midlands      8
## 228  2020-03-18                 Midlands     13
## 229  2020-03-19                 Midlands      8
## 230  2020-03-20                 Midlands     28
## 231  2020-03-21                 Midlands     13
## 232  2020-03-22                 Midlands     31
## 233  2020-03-23                 Midlands     33
## 234  2020-03-24                 Midlands     41
## 235  2020-03-25                 Midlands     48
## 236  2020-03-26                 Midlands     64
## 237  2020-03-27                 Midlands     72
## 238  2020-03-28                 Midlands     89
## 239  2020-03-29                 Midlands     92
## 240  2020-03-30                 Midlands     90
## 241  2020-03-31                 Midlands    123
## 242  2020-04-01                 Midlands    140
## 243  2020-04-02                 Midlands    142
## 244  2020-04-03                 Midlands    124
## 245  2020-04-04                 Midlands    151
## 246  2020-04-05                 Midlands    164
## 247  2020-04-06                 Midlands    140
## 248  2020-04-07                 Midlands    123
## 249  2020-04-08                 Midlands    186
## 250  2020-04-09                 Midlands    139
## 251  2020-04-10                 Midlands    127
## 252  2020-04-11                 Midlands    142
## 253  2020-04-12                 Midlands    139
## 254  2020-04-13                 Midlands    120
## 255  2020-04-14                 Midlands    116
## 256  2020-04-15                 Midlands    147
## 257  2020-04-16                 Midlands    102
## 258  2020-04-17                 Midlands    118
## 259  2020-04-18                 Midlands    115
## 260  2020-04-19                 Midlands     92
## 261  2020-04-20                 Midlands    107
## 262  2020-04-21                 Midlands     86
## 263  2020-04-22                 Midlands     78
## 264  2020-04-23                 Midlands    103
## 265  2020-04-24                 Midlands     79
## 266  2020-04-25                 Midlands     72
## 267  2020-04-26                 Midlands     81
## 268  2020-04-27                 Midlands     74
## 269  2020-04-28                 Midlands     68
## 270  2020-04-29                 Midlands     53
## 271  2020-04-30                 Midlands     56
## 272  2020-05-01                 Midlands     64
## 273  2020-05-02                 Midlands     51
## 274  2020-05-03                 Midlands     52
## 275  2020-05-04                 Midlands     61
## 276  2020-05-05                 Midlands     58
## 277  2020-05-06                 Midlands     59
## 278  2020-05-07                 Midlands     48
## 279  2020-05-08                 Midlands     34
## 280  2020-05-09                 Midlands     37
## 281  2020-05-10                 Midlands     42
## 282  2020-05-11                 Midlands     33
## 283  2020-05-12                 Midlands     45
## 284  2020-05-13                 Midlands     39
## 285  2020-05-14                 Midlands     37
## 286  2020-05-15                 Midlands     40
## 287  2020-05-16                 Midlands     34
## 288  2020-05-17                 Midlands     31
## 289  2020-05-18                 Midlands     34
## 290  2020-05-19                 Midlands     34
## 291  2020-05-20                 Midlands     36
## 292  2020-05-21                 Midlands     32
## 293  2020-05-22                 Midlands     27
## 294  2020-05-23                 Midlands     34
## 295  2020-05-24                 Midlands     19
## 296  2020-05-25                 Midlands     26
## 297  2020-05-26                 Midlands     33
## 298  2020-05-27                 Midlands     29
## 299  2020-05-28                 Midlands     27
## 300  2020-05-29                 Midlands     20
## 301  2020-05-30                 Midlands     20
## 302  2020-05-31                 Midlands     21
## 303  2020-06-01                 Midlands     20
## 304  2020-06-02                 Midlands     21
## 305  2020-06-03                 Midlands     23
## 306  2020-06-04                 Midlands     15
## 307  2020-06-05                 Midlands     21
## 308  2020-06-06                 Midlands     19
## 309  2020-06-07                 Midlands     14
## 310  2020-06-08                 Midlands     15
## 311  2020-06-09                 Midlands     17
## 312  2020-06-10                 Midlands     14
## 313  2020-06-11                 Midlands     13
## 314  2020-06-12                 Midlands      6
## 315  2020-06-13                 Midlands      0
## 316  2020-03-01 North East and Yorkshire      0
## 317  2020-03-02 North East and Yorkshire      0
## 318  2020-03-03 North East and Yorkshire      0
## 319  2020-03-04 North East and Yorkshire      0
## 320  2020-03-05 North East and Yorkshire      0
## 321  2020-03-06 North East and Yorkshire      0
## 322  2020-03-07 North East and Yorkshire      0
## 323  2020-03-08 North East and Yorkshire      0
## 324  2020-03-09 North East and Yorkshire      0
## 325  2020-03-10 North East and Yorkshire      0
## 326  2020-03-11 North East and Yorkshire      0
## 327  2020-03-12 North East and Yorkshire      0
## 328  2020-03-13 North East and Yorkshire      0
## 329  2020-03-14 North East and Yorkshire      0
## 330  2020-03-15 North East and Yorkshire      2
## 331  2020-03-16 North East and Yorkshire      3
## 332  2020-03-17 North East and Yorkshire      1
## 333  2020-03-18 North East and Yorkshire      2
## 334  2020-03-19 North East and Yorkshire      6
## 335  2020-03-20 North East and Yorkshire      5
## 336  2020-03-21 North East and Yorkshire      6
## 337  2020-03-22 North East and Yorkshire      7
## 338  2020-03-23 North East and Yorkshire      9
## 339  2020-03-24 North East and Yorkshire      8
## 340  2020-03-25 North East and Yorkshire     18
## 341  2020-03-26 North East and Yorkshire     21
## 342  2020-03-27 North East and Yorkshire     28
## 343  2020-03-28 North East and Yorkshire     35
## 344  2020-03-29 North East and Yorkshire     38
## 345  2020-03-30 North East and Yorkshire     64
## 346  2020-03-31 North East and Yorkshire     60
## 347  2020-04-01 North East and Yorkshire     67
## 348  2020-04-02 North East and Yorkshire     74
## 349  2020-04-03 North East and Yorkshire    100
## 350  2020-04-04 North East and Yorkshire    105
## 351  2020-04-05 North East and Yorkshire     92
## 352  2020-04-06 North East and Yorkshire     96
## 353  2020-04-07 North East and Yorkshire    102
## 354  2020-04-08 North East and Yorkshire    107
## 355  2020-04-09 North East and Yorkshire    111
## 356  2020-04-10 North East and Yorkshire    117
## 357  2020-04-11 North East and Yorkshire     98
## 358  2020-04-12 North East and Yorkshire     84
## 359  2020-04-13 North East and Yorkshire     94
## 360  2020-04-14 North East and Yorkshire    107
## 361  2020-04-15 North East and Yorkshire     96
## 362  2020-04-16 North East and Yorkshire    103
## 363  2020-04-17 North East and Yorkshire     88
## 364  2020-04-18 North East and Yorkshire     95
## 365  2020-04-19 North East and Yorkshire     88
## 366  2020-04-20 North East and Yorkshire    100
## 367  2020-04-21 North East and Yorkshire     76
## 368  2020-04-22 North East and Yorkshire     84
## 369  2020-04-23 North East and Yorkshire     63
## 370  2020-04-24 North East and Yorkshire     72
## 371  2020-04-25 North East and Yorkshire     69
## 372  2020-04-26 North East and Yorkshire     65
## 373  2020-04-27 North East and Yorkshire     65
## 374  2020-04-28 North East and Yorkshire     57
## 375  2020-04-29 North East and Yorkshire     69
## 376  2020-04-30 North East and Yorkshire     57
## 377  2020-05-01 North East and Yorkshire     64
## 378  2020-05-02 North East and Yorkshire     48
## 379  2020-05-03 North East and Yorkshire     40
## 380  2020-05-04 North East and Yorkshire     49
## 381  2020-05-05 North East and Yorkshire     40
## 382  2020-05-06 North East and Yorkshire     50
## 383  2020-05-07 North East and Yorkshire     45
## 384  2020-05-08 North East and Yorkshire     42
## 385  2020-05-09 North East and Yorkshire     44
## 386  2020-05-10 North East and Yorkshire     40
## 387  2020-05-11 North East and Yorkshire     29
## 388  2020-05-12 North East and Yorkshire     27
## 389  2020-05-13 North East and Yorkshire     28
## 390  2020-05-14 North East and Yorkshire     30
## 391  2020-05-15 North East and Yorkshire     32
## 392  2020-05-16 North East and Yorkshire     35
## 393  2020-05-17 North East and Yorkshire     26
## 394  2020-05-18 North East and Yorkshire     29
## 395  2020-05-19 North East and Yorkshire     27
## 396  2020-05-20 North East and Yorkshire     21
## 397  2020-05-21 North East and Yorkshire     33
## 398  2020-05-22 North East and Yorkshire     22
## 399  2020-05-23 North East and Yorkshire     18
## 400  2020-05-24 North East and Yorkshire     25
## 401  2020-05-25 North East and Yorkshire     21
## 402  2020-05-26 North East and Yorkshire     21
## 403  2020-05-27 North East and Yorkshire     21
## 404  2020-05-28 North East and Yorkshire     20
## 405  2020-05-29 North East and Yorkshire     24
## 406  2020-05-30 North East and Yorkshire     20
## 407  2020-05-31 North East and Yorkshire     19
## 408  2020-06-01 North East and Yorkshire     16
## 409  2020-06-02 North East and Yorkshire     22
## 410  2020-06-03 North East and Yorkshire     22
## 411  2020-06-04 North East and Yorkshire     17
## 412  2020-06-05 North East and Yorkshire     17
## 413  2020-06-06 North East and Yorkshire     20
## 414  2020-06-07 North East and Yorkshire     13
## 415  2020-06-08 North East and Yorkshire     11
## 416  2020-06-09 North East and Yorkshire     11
## 417  2020-06-10 North East and Yorkshire     15
## 418  2020-06-11 North East and Yorkshire      4
## 419  2020-06-12 North East and Yorkshire      7
## 420  2020-06-13 North East and Yorkshire      2
## 421  2020-03-01               North West      0
## 422  2020-03-02               North West      0
## 423  2020-03-03               North West      0
## 424  2020-03-04               North West      0
## 425  2020-03-05               North West      1
## 426  2020-03-06               North West      0
## 427  2020-03-07               North West      0
## 428  2020-03-08               North West      1
## 429  2020-03-09               North West      0
## 430  2020-03-10               North West      0
## 431  2020-03-11               North West      0
## 432  2020-03-12               North West      2
## 433  2020-03-13               North West      3
## 434  2020-03-14               North West      1
## 435  2020-03-15               North West      4
## 436  2020-03-16               North West      2
## 437  2020-03-17               North West      4
## 438  2020-03-18               North West      6
## 439  2020-03-19               North West      7
## 440  2020-03-20               North West     10
## 441  2020-03-21               North West     11
## 442  2020-03-22               North West     13
## 443  2020-03-23               North West     16
## 444  2020-03-24               North West     21
## 445  2020-03-25               North West     21
## 446  2020-03-26               North West     29
## 447  2020-03-27               North West     35
## 448  2020-03-28               North West     28
## 449  2020-03-29               North West     46
## 450  2020-03-30               North West     67
## 451  2020-03-31               North West     52
## 452  2020-04-01               North West     86
## 453  2020-04-02               North West     96
## 454  2020-04-03               North West     95
## 455  2020-04-04               North West     98
## 456  2020-04-05               North West    102
## 457  2020-04-06               North West    100
## 458  2020-04-07               North West    134
## 459  2020-04-08               North West    127
## 460  2020-04-09               North West    119
## 461  2020-04-10               North West    117
## 462  2020-04-11               North West    139
## 463  2020-04-12               North West    126
## 464  2020-04-13               North West    129
## 465  2020-04-14               North West    131
## 466  2020-04-15               North West    114
## 467  2020-04-16               North West    134
## 468  2020-04-17               North West     98
## 469  2020-04-18               North West    113
## 470  2020-04-19               North West     71
## 471  2020-04-20               North West     83
## 472  2020-04-21               North West     76
## 473  2020-04-22               North West     86
## 474  2020-04-23               North West     85
## 475  2020-04-24               North West     66
## 476  2020-04-25               North West     65
## 477  2020-04-26               North West     55
## 478  2020-04-27               North West     54
## 479  2020-04-28               North West     57
## 480  2020-04-29               North West     62
## 481  2020-04-30               North West     59
## 482  2020-05-01               North West     45
## 483  2020-05-02               North West     56
## 484  2020-05-03               North West     55
## 485  2020-05-04               North West     48
## 486  2020-05-05               North West     48
## 487  2020-05-06               North West     44
## 488  2020-05-07               North West     49
## 489  2020-05-08               North West     42
## 490  2020-05-09               North West     30
## 491  2020-05-10               North West     41
## 492  2020-05-11               North West     34
## 493  2020-05-12               North West     38
## 494  2020-05-13               North West     25
## 495  2020-05-14               North West     26
## 496  2020-05-15               North West     33
## 497  2020-05-16               North West     32
## 498  2020-05-17               North West     24
## 499  2020-05-18               North West     31
## 500  2020-05-19               North West     35
## 501  2020-05-20               North West     27
## 502  2020-05-21               North West     26
## 503  2020-05-22               North West     26
## 504  2020-05-23               North West     31
## 505  2020-05-24               North West     26
## 506  2020-05-25               North West     31
## 507  2020-05-26               North West     27
## 508  2020-05-27               North West     27
## 509  2020-05-28               North West     28
## 510  2020-05-29               North West     20
## 511  2020-05-30               North West     17
## 512  2020-05-31               North West     13
## 513  2020-06-01               North West     12
## 514  2020-06-02               North West     27
## 515  2020-06-03               North West     21
## 516  2020-06-04               North West     20
## 517  2020-06-05               North West     15
## 518  2020-06-06               North West     23
## 519  2020-06-07               North West     17
## 520  2020-06-08               North West     19
## 521  2020-06-09               North West     15
## 522  2020-06-10               North West     12
## 523  2020-06-11               North West     14
## 524  2020-06-12               North West      4
## 525  2020-06-13               North West      0
## 526  2020-03-01               South East      0
## 527  2020-03-02               South East      0
## 528  2020-03-03               South East      1
## 529  2020-03-04               South East      0
## 530  2020-03-05               South East      1
## 531  2020-03-06               South East      0
## 532  2020-03-07               South East      0
## 533  2020-03-08               South East      1
## 534  2020-03-09               South East      1
## 535  2020-03-10               South East      1
## 536  2020-03-11               South East      1
## 537  2020-03-12               South East      0
## 538  2020-03-13               South East      1
## 539  2020-03-14               South East      1
## 540  2020-03-15               South East      5
## 541  2020-03-16               South East      8
## 542  2020-03-17               South East      7
## 543  2020-03-18               South East     10
## 544  2020-03-19               South East      9
## 545  2020-03-20               South East     14
## 546  2020-03-21               South East      7
## 547  2020-03-22               South East     25
## 548  2020-03-23               South East     20
## 549  2020-03-24               South East     22
## 550  2020-03-25               South East     29
## 551  2020-03-26               South East     34
## 552  2020-03-27               South East     34
## 553  2020-03-28               South East     36
## 554  2020-03-29               South East     54
## 555  2020-03-30               South East     58
## 556  2020-03-31               South East     65
## 557  2020-04-01               South East     66
## 558  2020-04-02               South East     55
## 559  2020-04-03               South East     72
## 560  2020-04-04               South East     80
## 561  2020-04-05               South East     82
## 562  2020-04-06               South East     88
## 563  2020-04-07               South East    100
## 564  2020-04-08               South East     83
## 565  2020-04-09               South East    104
## 566  2020-04-10               South East     88
## 567  2020-04-11               South East     88
## 568  2020-04-12               South East     88
## 569  2020-04-13               South East     84
## 570  2020-04-14               South East     65
## 571  2020-04-15               South East     72
## 572  2020-04-16               South East     56
## 573  2020-04-17               South East     86
## 574  2020-04-18               South East     57
## 575  2020-04-19               South East     70
## 576  2020-04-20               South East     86
## 577  2020-04-21               South East     50
## 578  2020-04-22               South East     54
## 579  2020-04-23               South East     57
## 580  2020-04-24               South East     64
## 581  2020-04-25               South East     51
## 582  2020-04-26               South East     51
## 583  2020-04-27               South East     40
## 584  2020-04-28               South East     40
## 585  2020-04-29               South East     47
## 586  2020-04-30               South East     29
## 587  2020-05-01               South East     37
## 588  2020-05-02               South East     36
## 589  2020-05-03               South East     17
## 590  2020-05-04               South East     35
## 591  2020-05-05               South East     29
## 592  2020-05-06               South East     25
## 593  2020-05-07               South East     27
## 594  2020-05-08               South East     26
## 595  2020-05-09               South East     28
## 596  2020-05-10               South East     19
## 597  2020-05-11               South East     25
## 598  2020-05-12               South East     27
## 599  2020-05-13               South East     18
## 600  2020-05-14               South East     32
## 601  2020-05-15               South East     24
## 602  2020-05-16               South East     22
## 603  2020-05-17               South East     18
## 604  2020-05-18               South East     22
## 605  2020-05-19               South East     12
## 606  2020-05-20               South East     22
## 607  2020-05-21               South East     14
## 608  2020-05-22               South East     17
## 609  2020-05-23               South East     21
## 610  2020-05-24               South East     16
## 611  2020-05-25               South East     13
## 612  2020-05-26               South East     19
## 613  2020-05-27               South East     17
## 614  2020-05-28               South East     12
## 615  2020-05-29               South East     18
## 616  2020-05-30               South East      8
## 617  2020-05-31               South East     10
## 618  2020-06-01               South East     11
## 619  2020-06-02               South East     12
## 620  2020-06-03               South East     17
## 621  2020-06-04               South East     11
## 622  2020-06-05               South East      9
## 623  2020-06-06               South East      9
## 624  2020-06-07               South East     11
## 625  2020-06-08               South East      5
## 626  2020-06-09               South East      9
## 627  2020-06-10               South East      8
## 628  2020-06-11               South East      3
## 629  2020-06-12               South East      5
## 630  2020-06-13               South East      0
## 631  2020-03-01               South West      0
## 632  2020-03-02               South West      0
## 633  2020-03-03               South West      0
## 634  2020-03-04               South West      0
## 635  2020-03-05               South West      0
## 636  2020-03-06               South West      0
## 637  2020-03-07               South West      0
## 638  2020-03-08               South West      0
## 639  2020-03-09               South West      0
## 640  2020-03-10               South West      0
## 641  2020-03-11               South West      1
## 642  2020-03-12               South West      0
## 643  2020-03-13               South West      0
## 644  2020-03-14               South West      1
## 645  2020-03-15               South West      0
## 646  2020-03-16               South West      0
## 647  2020-03-17               South West      2
## 648  2020-03-18               South West      2
## 649  2020-03-19               South West      5
## 650  2020-03-20               South West      3
## 651  2020-03-21               South West      6
## 652  2020-03-22               South West      9
## 653  2020-03-23               South West      9
## 654  2020-03-24               South West      7
## 655  2020-03-25               South West      9
## 656  2020-03-26               South West     11
## 657  2020-03-27               South West     13
## 658  2020-03-28               South West     21
## 659  2020-03-29               South West     18
## 660  2020-03-30               South West     23
## 661  2020-03-31               South West     23
## 662  2020-04-01               South West     22
## 663  2020-04-02               South West     23
## 664  2020-04-03               South West     30
## 665  2020-04-04               South West     42
## 666  2020-04-05               South West     32
## 667  2020-04-06               South West     34
## 668  2020-04-07               South West     39
## 669  2020-04-08               South West     47
## 670  2020-04-09               South West     24
## 671  2020-04-10               South West     46
## 672  2020-04-11               South West     43
## 673  2020-04-12               South West     23
## 674  2020-04-13               South West     27
## 675  2020-04-14               South West     24
## 676  2020-04-15               South West     32
## 677  2020-04-16               South West     29
## 678  2020-04-17               South West     33
## 679  2020-04-18               South West     25
## 680  2020-04-19               South West     31
## 681  2020-04-20               South West     26
## 682  2020-04-21               South West     26
## 683  2020-04-22               South West     23
## 684  2020-04-23               South West     17
## 685  2020-04-24               South West     19
## 686  2020-04-25               South West     15
## 687  2020-04-26               South West     27
## 688  2020-04-27               South West     13
## 689  2020-04-28               South West     17
## 690  2020-04-29               South West     15
## 691  2020-04-30               South West     26
## 692  2020-05-01               South West      6
## 693  2020-05-02               South West      7
## 694  2020-05-03               South West     10
## 695  2020-05-04               South West     17
## 696  2020-05-05               South West     14
## 697  2020-05-06               South West     19
## 698  2020-05-07               South West     16
## 699  2020-05-08               South West      6
## 700  2020-05-09               South West     11
## 701  2020-05-10               South West      5
## 702  2020-05-11               South West      8
## 703  2020-05-12               South West      7
## 704  2020-05-13               South West      7
## 705  2020-05-14               South West      6
## 706  2020-05-15               South West      4
## 707  2020-05-16               South West      4
## 708  2020-05-17               South West      6
## 709  2020-05-18               South West      4
## 710  2020-05-19               South West      6
## 711  2020-05-20               South West      1
## 712  2020-05-21               South West      9
## 713  2020-05-22               South West      6
## 714  2020-05-23               South West      6
## 715  2020-05-24               South West      3
## 716  2020-05-25               South West      8
## 717  2020-05-26               South West     11
## 718  2020-05-27               South West      5
## 719  2020-05-28               South West      9
## 720  2020-05-29               South West      4
## 721  2020-05-30               South West      3
## 722  2020-05-31               South West      2
## 723  2020-06-01               South West      6
## 724  2020-06-02               South West      2
## 725  2020-06-03               South West      5
## 726  2020-06-04               South West      2
## 727  2020-06-05               South West      2
## 728  2020-06-06               South West      1
## 729  2020-06-07               South West      3
## 730  2020-06-08               South West      3
## 731  2020-06-09               South West      0
## 732  2020-06-10               South West      0
## 733  2020-06-11               South West      2
## 734  2020-06-12               South West      2
## 735  2020-06-13               South West      0

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2020-06-14"

The completion date of the NHS Pathways data is Sunday 14 Jun 2020.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -8.7147  -2.1978  -0.4288   2.3486   4.4971  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 5.017e+00  5.240e-02   95.75   <2e-16 ***
## note_lag    1.106e-05  5.149e-07   21.48   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 9.547593)
## 
##     Null deviance: 4757.11  on 43  degrees of freedom
## Residual deviance:  413.95  on 42  degrees of freedom
##   (23 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 4

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##  150.975634    1.000011
exp(confint(lag_mod))
##                 2.5 %     97.5 %
## (Intercept) 136.09359 167.128405
## note_lag      1.00001   1.000012

Rsq(lag_mod)
## [1] 0.9129832

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                            sysname 
##                                                                                           "Darwin" 
##                                                                                            release 
##                                                                                           "19.5.0" 
##                                                                                            version 
## "Darwin Kernel Version 19.5.0: Tue May 26 20:41:44 PDT 2020; root:xnu-6153.121.2~2/RELEASE_X86_64" 
##                                                                                           nodename 
##                                                                                   "Mac-1467.local" 
##                                                                                            machine 
##                                                                                           "x86_64" 
##                                                                                              login 
##                                                                                             "root" 
##                                                                                               user 
##                                                                                           "runner" 
##                                                                                     effective_user 
##                                                                                           "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin15.6.0   
## arch           x86_64                      
## os             darwin15.6.0                
## system         x86_64, darwin15.6.0        
## status                                     
## major          3                           
## minor          6.3                         
## year           2020                        
## month          02                          
## day            29                          
## svn rev        77875                       
## language       R                           
## version.string R version 3.6.3 (2020-02-29)
## nickname       Holding the Windsock

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 3.6.3 (2020-02-29)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS Catalina 10.15.5
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.1     ggpubr_0.3.0         lubridate_1.7.9     
##  [4] chngpt_2020.5-21     cyphr_1.1.0          DT_0.13             
##  [7] kableExtra_1.1.0     janitor_2.0.1        remotes_2.1.1       
## [10] projections_0.4.1    earlyR_0.0.1         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.1      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.5          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.0        stringr_1.4.0       
## [22] dplyr_1.0.0          purrr_0.3.4          readr_1.3.1         
## [25] tidyr_1.1.0          tibble_3.0.1         ggplot2_3.3.1       
## [28] tidyverse_1.3.0      here_0.1             reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] colorspace_1.4-1  selectr_0.4-2     ggsignif_0.6.0    ellipsis_0.3.1   
##  [5] rprojroot_1.3-2   snakecase_0.11.0  fs_1.4.1          rstudioapi_0.11  
##  [9] farver_2.0.3      fansi_0.4.1       splines_3.6.3     knitr_1.28       
## [13] jsonlite_1.6.1    broom_0.5.6       dbplyr_1.4.4      compiler_3.6.3   
## [17] httr_1.4.1        backports_1.1.7   assertthat_0.2.1  Matrix_1.2-18    
## [21] cli_2.0.2         htmltools_0.4.0   prettyunits_1.1.1 tools_3.6.3      
## [25] gtable_0.3.0      glue_1.4.1        Rcpp_1.0.4.6      carData_3.0-4    
## [29] cellranger_1.1.0  vctrs_0.3.1       nlme_3.1-144      matchmaker_0.1.1 
## [33] crosstalk_1.1.0.1 xfun_0.14         ps_1.3.3          openxlsx_4.1.5   
## [37] lifecycle_0.2.0   rstatix_0.5.0     MASS_7.3-51.5     scales_1.1.1     
## [41] hms_0.5.3         sodium_1.1        yaml_2.2.1        curl_4.3         
## [45] gridExtra_2.3     stringi_1.4.6     kyotil_2019.11-22 boot_1.3-24      
## [49] pkgbuild_1.0.8    zip_2.0.4         rlang_0.4.6       pkgconfig_2.0.3  
## [53] evaluate_0.14     lattice_0.20-38   labeling_0.3      htmlwidgets_1.5.1
## [57] cowplot_1.0.0     processx_3.4.2    tidyselect_1.1.0  plyr_1.8.6       
## [61] magrittr_1.5      R6_2.4.1          generics_0.0.2    DBI_1.1.0        
## [65] pillar_1.4.4      haven_2.3.1       foreign_0.8-75    withr_2.2.0      
## [69] mgcv_1.8-31       survival_3.1-8    abind_1.4-5       modelr_0.1.8     
## [73] crayon_1.3.4      car_3.0-8         utf8_1.1.4        rmarkdown_2.2    
## [77] viridis_0.5.1     grid_3.6.3        readxl_1.3.1      data.table_1.12.8
## [81] blob_1.2.1        callr_3.4.3       reprex_0.3.0      digest_0.6.25    
## [85] webshot_0.5.2     munsell_0.5.0     viridisLite_0.3.0